A theorem on majorizing measures
成果类型：
Article
署名作者：
Bednorz, Witold
署名单位：
University of Warsaw
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117906000000241
发表日期：
2006
页码：
1771-1781
关键词：
摘要：
Let (T,d) be a metric space and phi:R+ -> R an increasing, convex function with phi(0) = 0. We prove that if m is a probability measure m on T which is majorizing with respect to d, phi, that is, delta := sup(x epsilon T)integral(D(T))(0)phi(-1)(1/m(B(x, epsilon))) d epsilon < infinity, then E sup(s,t epsilon T)vertical bar X(s)-X(t)vertical bar <= 32 delta for each separable stochastic process X(t), t epsilon T, which satisfies E phi vertical bar X(s) - X(t)vertical bar/d(s,t) <= 1 for all s, t epsilon T, s not equal t. This is a strengthening of one of the main results from Talagrand [Ann. Probab. 18 (1990) 1-49], and its proof is significantly simpler.